This section is intended to introduce various aspects of the art, which may be associated with exemplary embodiments of the present invention. This discussion is believed to assist in providing a framework to facilitate a better understanding of particular aspects of the present invention. Accordingly, it should be understood that this section should be read in this light, and not necessarily as admissions of prior art.
An important goal of seismic prospecting is to accurately image subsurface structures commonly referred to as reflectors. Seismic prospecting is facilitated by obtaining raw seismic data during performance of a seismic survey. During a seismic survey, seismic energy can be generated at ground or sea level by, for example, a controlled explosion (or other form of source, such as vibrators), and delivered to the earth. Seismic waves are reflected from underground structures and are received by a number of sensors/receivers, such as geophones. The seismic data received by the geophones is processed in an effort to create an accurate mapping of the underground environment. The processed data is then examined with a goal of identifying geological formations that may contain hydrocarbons (e.g., oil and/or natural gas).
Full Wavefield Inversion (FWI) is a seismic method capable of utilizing the full seismic record, including the seismic events that are treated as “noise” by standard inversion algorithms. The goal of FWI is to build a realistic subsurface model by minimizing the misfit between the recorded seismic data and synthetic (or modeled) data obtained via numerical simulation.
FWI is a computer-implemented geophysical method that is used to invert for subsurface properties, such as velocity or acoustic impedance. The crux of any FWI algorithm can be described as follows: using a starting subsurface physical property model, synthetic seismic data are generated, i.e. modeled or simulated, by solving the wave equation using a numerical scheme (e.g., finite-difference, finite-element etc.). The term velocity model or physical property model as used herein refers to an array of numbers, typically a 3-D array, where each number, which may be called a model parameter, is a value of velocity or another physical property in a cell, where a subsurface region has been conceptually divided into discrete cells for computational purposes. The synthetic seismic data are compared with the field seismic data and using the difference between the two, an error or objective function is calculated. Using the objective function, a modified subsurface model is generated which is used to simulate a new set of synthetic seismic data. This new set of synthetic seismic data is compared with the field data to generate a new objective function. This process is repeated until the objective function is satisfactorily minimized and the final subsurface model is generated. A global or local optimization method is used to minimize the objective function and to update the subsurface model.
Current implementation of FWI utilizes a gradient-based local optimization technique to optimize the model parameters. The gradient-based inversion relies on computing the gradient of the mismatch objective functional. The tomographic term, obtained by cross-correlating the forward-scattered wavefields, mainly updates the long wavelength components of the model parameters, whereas the migration term, obtained by cross-correlating the backward-scattered wavefields, mainly updates the short wavelength components of the model parameters. Conventional FWI does not explicitly distinguish contributions of the tomographic and migration terms, and it implicitly combines these two terms with equal weights. This often results in the FWI gradient having a very weak tomographic term. This is especially true when the data lack low frequencies, and the reflectivity contrast of the media is relatively weak. The lack of the tomographic component in the gradient makes the conventional FWI ineffective in updating the background (the long wavelengths) of the model parameters. Therefore, in such situations, the inversion result is often oscillatory, exhibited by cycle skipping between the observed and simulated data. Cycle skipping is known to produce objective functions that have many local minima, which prevent commonly used optimization techniques (e.g., conjugate gradient optimization) from finding the true global minimum.
It has been well accepted that, for reflection dominant data, conventional FWI (Tarantola, 1984) lacks the ability to update long wavelengths of the velocity model and requires a very accurate starting model to converge to a geologically meaningful result. If the conventional FWI starts with a relatively “poor” starting model, where the kinematic differences between the simulated data and the observed data are greater than half of the dominant wavelength, it often gets stuck in local minima because of cycle skipping. One fundamental reason of the failure is that for a typical seismic bandwidth, especially for the fact that low frequency data are lacking, the gradient of the conventional FWI at early iterations usually contains strong high-wavenumber information, but very weak mid- to low-wavenumber information. This high-wavenumber-biased characteristic of the gradient makes FWI update predominantly the short wavelengths, instead of the long wavelengths of the velocity model. This anchors the high wavenumber information (i.e., reflectivities) at the wrong position because of the wrong starting model (think about mis-positioned reflectors in migration due to a wrong migration velocity). The lack of the ability to generate sufficient long wavelength model updates and the freedom to move the mis-positioned high wavenumber information around, makes conventional FWI stuck in local minima.